SHEEP, a Signed Hamiltonian Eigenvector Embedding for Proximity

Journal article

Signed network embedding methods allow for a low-dimensional representation of nodes and primarily focus on partitioning the graph into clusters, hence losing information on continuous node attributes. Here, we introduce a spectral embedding algorithm for understanding proximal relationships between nodes in signed graphs, where edges can take either positive or negative weights. Inspired by a physical model, we construct our embedding as the minimum energy configuration of a Hamiltonian dependent on the distance between nodes and locate the optimal embedding dimension. We show through a series of experiments on synthetic and empirical networks, that our method (SHEEP) can recover continuous node attributes showcasing its main advantages: re-configurability into a computationally efficient eigenvector problem, retrieval of ground state energy which can be used as a statistical test for the presence of strong balance, and measure of node extremism, computed as the distance to the origin in the optimal embedding.

Authors: Babul, S; Lambiotte, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer Nature
• Journal: Communications Physics
• Volume: 7
• Issue: 1
• Article number: 8
• Publication date: 2024-01-04
• Acceptance date: 2023-12-14
• DOI: 10.1038/s42005-023-01504-6
• EISSN: 2399-3650
• Language: English
• Keywords: applied mathematics; complex networks